Generalized permutation matrix: Difference between revisions

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The abstract group of generalized permutation matrices is the [[wreath product]] of ''F''^× and ''S''_''n''. Concretely, this means that it is the [[semidirect product]] of Δ(''n'', ''F'') by the [[symmetric group]] ''S''_''n'':

:Δ(''n'', ''F'') {{unicode|⋉}} ''S''_''n'',

where ''S''_''n'' acts by permuting coordinates and the diagonal matrices Δ(''n'', ''F'') are isomorphic to the ''n''-fold product (''F''^×)^''n''.